MathDB

Emilia and Julieta have a pile of 2024 cards and play the following game: they take turns, and each player removes a number of cards that must be a power of two, i.e.,

1, 2, 4, 8, \dots

. The player who removes the last card wins. Julieta starts the game. Prove that there exists a strategy for Julieta that guarantees her victory, no matter how Emilia plays.

2

Problems(1)